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August 2020 On the eigenproblem for Gaussian bridges
Pavel Chigansky, Marina Kleptsyna, Dmytro Marushkevych
Bernoulli 26(3): 1706-1726 (August 2020). DOI: 10.3150/19-BEJ1157

Abstract

Spectral decomposition of the covariance operator is one of the main building blocks in the theory and applications of Gaussian processes. Unfortunately, it is notoriously hard to derive in a closed form. In this paper, we consider the eigenproblem for Gaussian bridges. Given a base process, its bridge is obtained by conditioning the trajectories to start and terminate at the given points. What can be said about the spectrum of a bridge, given the spectrum of its base process? We show how this question can be answered asymptotically for a family of processes, including the fractional Brownian motion.

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Pavel Chigansky. Marina Kleptsyna. Dmytro Marushkevych. "On the eigenproblem for Gaussian bridges." Bernoulli 26 (3) 1706 - 1726, August 2020. https://doi.org/10.3150/19-BEJ1157

Information

Received: 1 July 2017; Revised: 1 January 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193940
MathSciNet: MR4091089
Digital Object Identifier: 10.3150/19-BEJ1157

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 3 • August 2020
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